Riemann sums approximate the area between curves and the {{MATH_265}}-axis via rectangles. When computing this area via rectangles, there are several things to know: {{CMD_266}} {{CMD_267}} What interval are we on? In our discussion above we call this {{MATH_268}}. {{CMD_269}} How many rectangles will be used? In our discussion above we called this {{MATH_270}}. {{CMD_271}} What is the width of each individual rectangle? In our discussion above we called this {{MATH_272}}. {{CMD_273}} What points will determine the height of the rectangle? In our discussion above we called these sample points, {{MATH_274}}, and they can be left-endpoints, right-endpoints, or midpoints. {{CMD_275}} What is the actual height of the rectangle? This will always be {{MATH_276}}. {{CMD_277}} We approximate the area {{MATH_278}} with a Riemann sum {{MATH_279}}. {{CMD_280}} As {{MATH_281}} gets bigger and bigger, {{MATH_282}} gets smaller and smaller, and approximation gets better and better. We compute the exact value of {{MATH_283}} by taking the limit of Riemann sums {{MATH_284}}. {{CMD_285}} {{CMD_286}}